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1

On solution of non-instantaneous impulsive Hilfer fractional integro-differential evolution system

Trivedi Gargi J., Shah Vishant, Sharma Jaita, Sanghvi Rajesh

Mathematica Applicanda

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2023

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Vol. 51, no. 1

33--50

EN

In this article, we have considered the non-instantaneous fractional integrodifferential evolution system with Hilfer fractional differential operator in the Banach space and discussed its existence results for the mild solution for the equation with local and non-local conditions. These results are obtained by applying the method of a C0 operator generated by the linear part of the equation combined with the concept of nonlinear functional analysis and the fixed point theorems. We have discussed the examples to highlight the applicability of the results.

PL

Artykuł poświęcony jest ułamkowym, z opóźnieniem, systemom ewolucji całkowo-różniczkowej opisanym ułamkowym operatorem różniczkowym Hilfera w przestrzeni Banacha. Analizowane jest istnienia gładkiego rozwiązania równania z warunkami lokalnymi i nielokalnymi. Wyniki uzyskano stosując do operatora C0 generowanego przez liniową część równania metody nieliniowej analizy funkcjonalnej z twierdzeniami o punkcie stałym. Zamieszczone przykłady podkreślają znaczenie otrzymanych wyników.

2

Nonnegative solutions for a class of semipositone nonlinear elliptic equations in bounded domains of Rn

Bachar Imed, Mâagli Habib, Eltayeb Hassan

Opuscula Mathematica

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2022

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Vol. 42, no. 6

793--803

EN

In this paper, we obtain sufficient conditions for the existence of a unique nonnegative continuous solution of semipositone semilinear elliptic problem in bounded domains of Rn (n ≥ 2). The global behavior of this solution is also given.

3

Existence and Ulam-Hyers stability of the implicit fractional boundary value problem with ψ-Caputo fractional derivative

Wahash Hanan A., Abdo Mohammed S, Panchal Satish K.

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 1

89--101

EN

In this paper, we investigate the existence, uniqueness and Ulam-Hyers stability of solutions for nonlinear implicit fractional differential equations with boundary conditions involving a ψ-Caputo fractional derivative. The obtained results for the proposed problem are proved under a new approach and minimal assumptions on the function ƒ. The analysis is based upon the reduction of the problem considered to the equivalent integral equation, while some fixed point theorems of Banach and Schauder and generalized Gronwall inequality are employed to obtain our results for the problem at hand. Finally, the investigation is illustrated by providing a suitable example.

4

Stability of an additive-quadratic-quartic functional equation

Kim Gwang Hui, Lee Yang-Hi

Demonstratio Mathematica

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2020

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Vol. 53, nr 1

1--7

EN

In this paper, we investigate the stability of an additive-quadratic-quartic functional equation f(x+2y)+f(x-2y) - 2f(x+y) - 2f(-x-y) - 2f(x-y) - 2f(y-x)+4f(-x)+2f(x) - f(2y) - f(-2y)+4f(y)+4f(-y)=0 by the direct method in the sense of Găvruta.

5

Existence results of noninstantaneous impulsive fractional integro-differential equation

Kataria Haribhai R., Patel Prakashkumar H., Shah Vishant

Demonstratio Mathematica

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2020

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Vol. 53, nr 1

373--384

EN

Existence of mild solution for noninstantaneous impulsive fractional order integro-differential equations with local and nonlocal conditions in Banach space is established in this paper. Existence results with local and nonlocal conditions are obtained through operator semigroup theory using generalized Banach contraction theorem and Krasnoselskii’s fixed point theorem, respectively. Finally, illustrations are added to validate derived results.

6

The existence of monotonic solutions of a class of quadratic integral equations of Volterra type

Karakurt Osman, Temizer Ӧmer Faruk

Journal of Mathematics and Applications

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2019

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Vol. 42

117--133

EN

Using the technique associated with measure of noncompactness we prove the existence of monotonic solutions of a class of quadratic integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval.

7

Fixed point theorems for monotone mappings in ordered Banach spaces under weak topology features

Alahmari Abdullah, Mabrouk Mohamed, Taoudi Mohamed-Aziz

Journal of Mathematics and Applications

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2019

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Vol. 42

5--19

EN

We present several fixed point theorems for monotone nonlinear operators in ordered Banach spaces. The main assumptions of our results are formulated in terms of the weak topology. As an application, we study the existence of solutions to a class of first-order vectorvalued ordinary differential equations. Our conclusions generalize many well-known results.

8

Existence and Ulam stability for nonlinear implicit differential equations with Riemann-Liouville fractional derivative

Benchohra Mouffak, Bouriah Soufyane, Nieto Juan J.

Demonstratio Mathematica

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2019

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Vol. 52, nr 1

437--450

EN

In this paper, we establish the existence and uniqueness of solutions for a class of initial value problem for nonlinear implicit fractional differential equations with Riemann-Liouville fractional derivative, also, the stability of this class of problem. The arguments are based upon the Banach contraction principle and Schaefer’s fixed point theorem. An example is included to show the applicability of our results.

9

Convergence and stability of Fibonacci-Mann iteration for a monotone non-Lipschitzian mapping

Aggarwal Sajan, Uddin Izhar

Demonstratio Mathematica

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2019

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Vol. 52, nr 1

388--396

EN

In this paper, we prove strong convergence and ∆-convergence of Fibonacci-Mann iteration for a monotone non-Lipschitzian mapping (i.e. nearly asymptotically nonexpansive mapping) in partially ordered hyperbolic metric space. Moreover, we prove stability of Fibonacci-Mann iteration. Further, we construct a numerical example to illustrate results. Our results simultaneously generalize the results of Alfuraidan and Khamsi [Bull. Aust. Math. Soc., 2017, 96, 307-316] and Schu [J. Math. Anal. Appl., 1991, 58, 407-413].

10

Positive solution of a fractional differential equation with integral boundary conditions

Abdo M. S., Wahash H. A., Panchal S. K.

Journal of Applied Mathematics and Computational Mechanics

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2018

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Vol. 17, nr 3

5--15

EN

In this paper, we prove the existence and uniqueness of a positive solution for a boundary value problem of nonlinear fractional differential equations involving a Caputo fractional operator with integral boundary conditions. The technique used to prove our results depends on the upper and lower solution, the Schauder fixed point theorem and the Banach contraction principle. The result of existence obtained through constructing the upper and lower control functions of the nonlinear term without any monotone requirement.

11

Non-Archimedean hyperstability of Cauchy-Jensen functional equations on a restricted domain

EL-Fassi I.

Journal of Applied Analysis

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2018

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Vol. 24, nr 2

155--165

EN

Let X be a normed space, U ⊂ X \ {0} a non-empty subset, and (G, +) a commutative group equipped with a complete ultrametric d that is invariant (i.e., d(x + z, y + z) = d(x, y) for x, y, z ∈ G). Under some weak natural assumptions on U and on the function γ : U3 → [0, ∞), we study the new generalized hyperstability results when f : U → G satisfies the inequality d(αf( x + y / α + z), αf(z) + f(y) + f(x)) ≤ γ(x, y, z) for all x, y, z ∈ U, where x+y α + z ∈ U and α ≥ 2 is a fixed positive integer. The method is based on a quite recent fixed point theorem (Theorem 1 in [J. Brzdęk and K. Ciepliński, A fixed point approach to the stability of functional equations in non-Archimedean metric spaces, Nonlinear Anal. 74 (2011), no. 18, 6861-6867]) in some functions spaces.

12

Positive solution for nonlinear fractional differential equation with integral boundary value condition

Zatla Y. T., Daudi-Merzagui N.

Fasciculi Mathematici

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2018

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Nr 61

163--177

EN

In this paper, we consider a fractional differential equation, with integral boundary conditions, when the nonlinearities are sign changing. Our approach is based on the Krasnoselskii theorem in double cones. We generalize some recent results.

13

Stability and hyperstability of a quadratic functional equation and a characterization of inner product spaces

EL-Fassi I., Park C., Kim G. H.

Demonstratio Mathematica

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2018

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Vol. 51, nr 1

295--303

EN

We have proved the Hyers-Ulam stability and the hyperstability of the quadratic functional equation f(x+y+z) +f(x+y−z) +f(x−y+z) +f(−x+y+z) = 4[f(x) +f(y) +f(z) ] in the class of functions from an abelian group G into a Banach space.

14

Measures of noncompactness in a Banach algebra and their applications

Dudek S.

Journal of Mathematics and Applications

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2017

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Vol. 40

69--84

EN

In this paper we study the existence of solutions of a nonlinear quadratic integral equation of fractional order. This equation is considered in the Banach space of real functions defined, continuous and bounded on the real half axis. Additionally, using the technique of measures of noncompactness we obtain some characterization of considered integral equation. We provide also an example illustrating the applicability of our approach.

15

The controllability of nonlinear implicit fractional delay dynamical systems

Joice Nirmala R., Balachandran K.

International Journal of Applied Mathematics and Computer Science

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2017

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Vol. 27, no. 3

501--513

EN

This paper is concerned with the controllability of nonlinear fractional delay dynamical systems with implicit fractional derivatives for multiple delays and distributed delays in control variables. Sufficient conditions are obtained by using the Darbo fixed point theorem. Further, examples are given to illustrate the theory.

16

Multiple solutions to third-order differential equations with derivative dependence and deviating arguments

Jankowski T.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2016

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Vol. 20, No 1

85--98

EN

In this paper, we give some new results for multiplicity of positive (nonnegative) solutions for third-order differential equations with derivative dependence, deviating arguments and Stieltjes integral boundary conditions. We discuss our problem with advanced argument α and arbitrary β ∈ C([0,1],[0,1]), see problem (2). It means that argument β can change the character on [0,1], so β can be delayed in some set J¯⊂ [0,1] and advanced in [0,1] \ J¯. Four examples illustrate the main results

17

Approximate generalized derivations close to derivations in Lie C*-algebras

Eshaghi M., Abbaszadeh S.

Journal of Applied Analysis

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2015

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Vol. 21, nr 1

37--43

EN

We apply a fixed point theorem to prove that there exists a unique derivation close to an approximately generalized derivation in Lie C*-algebras. Also, we prove the hyperstability of generalized derivations. In other words, we find some conditions under which an approximately generalized derivation becomes a derivation.

18

Controllability of nonlinear implicit fractional integrodifferential systems

Balachandran K., Divya S.

International Journal of Applied Mathematics and Computer Science

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2014

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Vol. 24, no. 4

713--722

EN

In this paper, we study the controllability of nonlinear fractional integrodifferential systems with implicit fractional derivative. Sufficient conditions for controllability results are obtained through the notion of the measure of noncompactness of a set and Darbo’s fixed point theorem. Examples are included to verify the result.

19

A general fixed point theorem on G-metric spaces

Dung N.V.

Fasciculi Mathematici

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2014

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Nr 52

35--43

EN

In this paper, we prove a general fixed point theorem on G-metric spaces by an implicit relation. This result unifies many fixed point theorems in [3], [6], [9], [12].

20

Fixed points of F-weak contractions on complete metric spaces

Wardowski D., Dung N.V.

Demonstratio Mathematica

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2014

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Vol. 47, nr 1

147--155

EN

In this paper, we introduce the notion of an F-weak contraction and prove a fixed point theorem for F-weak contractions. Examples are given to show that our result is a proper extension of some results known in the literature.